4 papers
Two-Dimensional Finite-Gap Schrodinger Operators as Limits of Two-Dimensional Integrable Difference Operators
P. A. Leonchik, G. S. Mauleshova, A. E. Mironov
In this paper we study two-dimensional discrete operators whose eigenfunctions at zero energy level are given by rational functions on spectral curves. We extend discrete operators…
Positive one-point commuting difference operators
Gulnara S. Mauleshova, Andrey E. Mironov
In this paper we study commuting difference operators containing a shift operator with only positive degrees. We construct examples of such operators in the case of hyperelliptic s…
On Rank Two Algebro--Geometric Solutions of an Integrable Chain
Gulnara S. Mauleshova, Andrey E. Mironov
In this paper we consider a differential--difference system which is equivalent to the commutativity condition of two differential--difference operators. We study the rank two alge…
Difference Krichever-Novikov operators
Gulnara S. Mauleshova, Andrey E. Mironov
In this paper we study commuting difference operators of rank two. We introduce an equation on potentials of the difference operator and som…